Kinetic study of Fe & Co perovskite catalyst in Fischer–Tropsch synthesis

The investigation of the reaction's kinetics is one of the most crucial aspects of the design of a commercial process. The current research investigates the kinetics of Fischer–Tropsch synthesis using a perovskite catalyst. The LaFe0.7 Co0.3 O3 perovskite catalyst was prepared via the thermal sol–gel technique and characterized using BET, XRD, SEM, and H2-TPR techniques. According to operating conditions (e.g. H2/CO: 1–2, pressure: 10–20 barg, temperature: 240–300 °C, and GHSV: 3000 1/h), Fischer–Tropsch reaction kinetics (CO conversion) were carried out in a fixed-bed reactor. Using the framework of Langmuir–Hinshelwood–Hougen–Watson (LHHW) theories, 18 kinetic expressions for CO conversion were derived, and all were fitted to experimental data one by one to determine the optimum condition. The correlation was derived from experimental data and well-fitted using LHHW form (according to the enol mechanism, carbon monoxide and dissociated hydrogen atoms are adsorbed and reacted on the surface of the catalyst) −rCO = kpbCOPCO(bH2PH2)0.5/(1 + bCOPCO + (bH2PH2)0.5)2. Finally, the activation energy of the optimum kinetic model was determined with respect to the Arrhenius equation under various operating conditions. The activation energy of perovskite catalyst is about 106.25 kJ/mol at temperatures 240–300 °C, pressures 10–20 barg, and H2/CO ratios 1–2, which is lower than other types of catalyst. Therefore, the catalyst was activated at a high temperature and demonstrated stable performance without any temperature runaway and coking issues.


Catalyst preparation
There are various methods for preparing perovskite oxide such as hydrothermal, microwave, precipitation, sol-gel, etc. 26 .The La Fe 0.7 Co 0.3 O 3 perovskite catalyst was prepared using the thermal sol-gel method.The catalyst was synthesized at room temperature by an aqueous solution of La(NO 3 )0.6H 2 O, Co(NO 3 )0.6H 2 O, and Fe(NO 3 )0.9H 2 O, then glycine solution was added drop wise to form the gel 27,28 .The prepared gel was dried at 180 °C for 4 h in the oven, and then calcinated in a furnace at 550 °C (5 °C/min) for 5 h.The sample was pressed into pellets, crushed, and sieved to obtain particles in size between the 40-60 ASTM mesh.

Catalyst characterization
The XRD measurement was carried out using the Philips PW1729 system.The diffraction pattern was obtained using a CuKα lamp with wavelength λ = 1.542°A in the angle range 2θ = 1 to 2θ = 80 and a step size of 0.06.The size of the particle crystals is calculated based on the XRD information and using the Scherer equation.Brunner Emmett Teller (BET) surface area, pore volume and mean pore diameter of the catalyst were determined using an ASAP 3020 instrument of Micrometrics.The SEM images were recorded using MIRA3 Tescan.Temperature Programmed Reduction (TPR) was carried out on 0.011 g of catalyst heated from 28 to 750 °C (20 °C/min) under 5% H 2 in Argon (total gas flow: 50 Ncc/min) with Chembet 3000 system.A CM120 microscope manufactured by Philips did the Transmission Electron Microscopy (TEM) test on the catalysts.

Catalyst activity measurement
The kinetic tests were performed in a fixed bed reactor using LaFe 0.7 Co 0.3 O 3 catalyst for Fischer Tropsch synthesis.The reactor was made of stainless steel with an 8 mm diameter and 700 mm height.The amount of 1 g catalyst is loaded into one-third of the reactor.The set-up consisted of 3 units: a feeding unit, a reaction unit, and a product separation and analysis unit. Figure 1 shows the schematic of the FT set-up.
The catalyst performance was tested under pressure and temperature ranges of 10-20 bar and 240-300 °C, respectively.The feed consisted of carbon monoxide and hydrogen with a percentage of 50% and 50%, respectively.The experimental results are reported in Table 3.The reactor temperature is controlled by a furnace equipped with a temperature controller located around the reactor to maintain a uniform temperature.To prevent choking of the reactor's outlet in case of the formation of heavy hydrocarbons, the reactor system is equipped with two hot and cold traps to collect light and heavy liquid products.The liquid products are discharged from the traps and gas products are sent to the GC (Agilent 7890) by a stainless steel tube.The feed has three mass flow controllers (MFCs): hydrogen, carbon monoxide, and nitrogen gases.The feed was preheated prior to entering the reactor.The reactor's pressure is adjusted using a pressure valve (Groove) installed before the outlet (Fig. 1).
After loading the catalyst in the reactor, to reduce the catalyst, the mixture of hydrogen and nitrogen gases with a ratio of 1 to 10 (H 2 / N 2 = 1/10) under atmospheric pressure at 450 °C for 24 h passes throughout the catalyst bed.However, developing kinetic equations requires a series of experiments in specific operating conditions.The intrinsic rate equations were estimated by comparing the theoretical and experimental rates.To determine the kinetic equation in a fixed bed reactor, several factors should be considered as follows 19,29,30 : • Catalyst activity should not be reduced.
• The temperature of the reactor should be constant (Due to the exothermic nature of the Fischer reaction, the operating conditions of the reaction should be considered in such a way that the CO conversion is low.)• No mass transfer limitation is implied in the calculations.However, to determine the kinetic equation under laboratory conditions, the velocity must be assumed to be uniform along the length of the reactor.Regarding the above assumption, the operating conditions should be www.nature.com/scientificreports/implemented in such a way that the CO conversion becomes less than 15%.In these situations, the reaction rate through the reactor is constant and the following equation can be used: The average rate is: In order to simplify the kinetics equations, the mass transfer resistance was relinquished from calculations.
According to the ideal gas low the partial pressure of each component calculated as blow:

Catalyst characterization results
The X-ray diffraction (XRD) of the prepared LaFe 0.7 Co 0.3 O 3 is presented in Fig. 2a.The catalyst was calcinated at 550 °C and XRD determined the crystal structure.According to Fig. 2 the diffraction peaks of the perovskite structure in the range of 2θ = 30-40 are sharpened, and it is proved that the perovskite structure was formed.
The used catalyst was characterized using XRD technique to identify the changes in its structure (Fig. 2b).The size of the LaFe 0.7 Co 0.3 O 3 crystals was calculated according to X-ray diffraction data with Scherer's equation 31 : Scherer modified another correlation to calculate the size of crystals 31 : (1) According to Scherer's equation, the average particle size was 30.69.The Ln(β) vs. Ln(1/cosθ) line graph was depicted for the LaFe 0.7 Co 0.3 O 3 crystals using the modified Scherer correlation (Fig. 3).According to the correlation, the predicted size is 33.81.The size difference between the two predicted models is less than 4. Hence, the error percentage is insignificant, so both correlations are acceptable, but the modified Scherer is more compatible than others.
The BET test was performed to determine the specific surface area of the catalyst after calcination at 550 °C (Table 2).Whereas, the surface area of the perovskite catalysts is low, but its strong structure makes it valuable.
Figure 4 represents the hydrogen consumption of the catalyst after the calcination process.As reported in Fig. 4 there are two reduction peaks between 2000 and 4000 s.The current result is inline with previous studies 11,[32][33][34] .The first reduction trend appears at low temperatures, roughly 280 °C in the 2500 s, while the second trend appears at temperatures between 380 and 430 °C in the 4200 s.Two peaks in the TPR profile reflect the two reducible cations in the B site (Fe and Co) 11 .
SEM images in Fig. 5a show that porous particles were formed and the EDXS proved that the actual composition of the catalyst is LaFe 0.67 Co 0.32 O 3 (Fig. 5b).

Ln(β)
Ln(1/cosθ)   www.nature.com/scientificreports/TEM observation of samples shows good distributions of grains of catalysts (Fig. 6).The results show that the particle size is between 20 and 140 nm, and the asymmetric shape of the grains proves that the XRD pattern is accurate.

Kinetic model
The main goal of the current research is to develop an appropriate kinetic model to predict the behavior of the perovskite catalyst (LaFe 0.7 Co 0.3 O 3 ) used for the Fischer-Tropsch process.The most crucial aspect of the FT process is elucidating the mechanism of the reaction.Moreover, the mechanisms were determined using various adsorption possibilities of CO and H 2 molecules on the catalyst's surface.There are four mechanisms for FT synthesis, such as carbide, enolic, alkyl, and alkenyl 23,35,36 .However, the main difference between the mechanisms is the monomer formation; the monomer formation stage was used to estimate the reaction rate.
The activity of LaFe 0.7 CO 0.3 O 3 perovskite catalyst was studied (Fig. 7) and the results show that after 50 h, the catalyst activity was stable.Additionally, in order to mitigate the impact of deactivation, new catalysts were loaded into each experiment.Therefore the kinetic data is reliable.The product selectivity at the temperature of 553 K and pressure of 20 bar within the catalyst activity range is reported (Fig. 8).The results show that the selectivity of C 5 + is in good agreement with previous studies 8 .Table 3 shows the elementary reaction sets for FT synthesis.The reaction rate expressions for the FTS based on elementary reactions are shown in Table 4.In the current study, to derive all reaction rates, represented in Table 5, the Langmuir-Hinshelwood-Hougen-Watson  www.nature.com/scientificreports/(LHHW) approach was applied accordingly.In addition, using polymath software, a suitable kinetic model was developed by fitting whole reaction rates against empirical data, and finally, the best kinetic model was chosen based on R 2 , R msd , and MARR.The most appropriate reaction rate (R 2 ) should be close to 1.Moreover, R msd and MARR might have a minimum value.The statistical parameters were determined as follows: 1. Square of the coefficient of correlation function (R 2 ): 2. Root Mean Square Deviation (R msd )

Mean Absolute Relative Residual (MARR):
Comparing experimental data to the model equation demonstrates that the FT-VII (3) model is in good agreement with the empirical results.In this scenario, carbon monoxide and hydrogen atoms are reacted while adsorbed on the surface of a catalyst.
Vol:.( 1234567890 The constant coefficient and validation parameters are estimated and presented in Table 6.The MARR percentage of the FT-VII(3) model is 9.65.The model, however, shows less deviation from the experimental data and is consistent with it.The MARR% values of the other obtained kinetic models are presented in Table 7; as it was shown, the FT-VII(3) model having the minimal MARR value fits the experimental data well.The best-fitted kinetic model is an enolic mechanism; in this mechanism, the base component (CHOH) is formed by partial   42,43 , the enolic mechanism is much better than the carbide mechanism for bimetallic oxide catalysts.
In addition, Fig. 9 depicts the comparison between experimental data and the calculated CO consumption rate.Polymath software shows that the experimental and calculated rates were close together and at some point, the experimental and calculated data were overlapped.
The reaction rate is determined using the model equation and compared with the empirical data (Fig. 10a  and b).The compatibility between the model and the experimental data is demonstrated by the closeness of the data to the straight line and the symmetry shape around the straight line.
In addition, Fig. 10b presents the calculated against the experimental reaction rate, and it shows that the calculated reaction rate is acceptable for predicting Fischer-Tropsch synthesis.The activation energy of a reaction is obtained by fitting data with the Arrhenius equation in various conditions.The activation energy of hydrocarbon formation is mostly between 75 to 110 kJ/mol [37][38][39] .In the current study, the activation energy value is 106.25 kJ/mol.which is close to activation energy reported previously 106.2 kJ/mol by abdollahi et al. and 100and 103 kJ/mol yange et al. and storch et al. [40][41][42] .Nevertheless, it was substantially higher than the value of 80.63 and 66.01 kJ/mol which are reported by davies et al. 43 and mansouri et al. 16 .Although the activation energy shows the importance of the diffusion interface, the high activation energies indicate the absence of diffusion effects in the Fischer-Tropsch reaction.Therefore, the pore diffusion restriction led to the low activation energy in the Fischer-Tropsch reaction.The pore size and catalyst structure correspond with the catalyst's preparation method and component 16,44 .

Conclusion
The performance of LaFe 0.7 Co 0.3 O 3 perovskite catalyst and kinetic of Fischer-Tropsch synthesis (CO conversion) were investigated in a fixed bed reactor under various operating conditions (e.g.H 2 /CO: 1-2, pressure: 10-20 barg, temperature: 240-300 °C, and GHSV: 3000 1/h).Several Langmuir-Hinshelwood-Hougen-Watson (LHHW) rate equations were derived.The unknown kinetic parameters such as R 2 , R msd , and MARR were estimated using empirical data in Polymath software.In addition, the kinetic parameters were estimated with non-linear regression and the results show that the FT-VII model predicts CO consumption with high compatibility.Finally, the activation energy was determined with respect to the Arrhenius equation and the optimum value of 106.25 kJ/mol was estimated under various operating conditions.The kinetic parameters correspond with the preparation method and catalyst component.Therefore, the perovskite catalyst is activated at a higher temperature, and consequently, the coking issue is diminished during the operation.

Figure 4 .
Figure 4. TPR profile of the perovskite catalyst.

Figure 6 .
Figure 6.TEM Pattern (a) Schematic of catalyst, and (b) particle size distribution.

Figure 7 .
Figure 7. Activity diagram during the time (a) CO convention (b) Hydrocarbon Selectivity.

Figure 8 .
Figure 8. Product selectivity of LaFeCoO catalyst at a temperature of 553 K and pressure of 20 bar.

Figure 10 .
Figure 10.The calculated vs. the experimental reaction rate (a) normal plot, (b) residual plot.
Surface area (m

Table 3 .
Experimental condition and results for kinetic tests.

Table 4 .
Elementary reaction sets for Fischer-Tropsch synthesis.

Table 6 .
Values of kinetic parameters of FT-VII(3) model.

Table 7 .
Parameters and mean absolute relative residuals (MARR) for the FT kinetic models.